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Numerical modeling of diffusion-induced deformation

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Abstract

We present a numerical approach to modeling the deformation induced by the Kirkendall effect in binary alloys. The governing equations for isothermal binary diffusion are formulated with respect to inert markers and also with respect to the volume-averaged velocity. Relations necessary to convert between the two formulations are derived. Whereas the marker formulation is the natural one in which to pose constitutive laws, the volume formulation provides certain computational advantages. We therefore compute the diffusion and deformation with respect to the volume-centered velocity and then determine the corresponding fields with respect to the markers. Several problems involving one-dimensional (1-D) diffusion couples are solved for verification, and a problem involving two-dimensional (2-D) diffusion in a lap joint is solved to illustrate the power of the method in a more complex geometry.

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Authors and Affiliations

  1. the Department of Mechanical and Industrial Engineering, University of Illinois at Urbana-Champaign, 61801, Urbana, IL, USA

    J. A. Dantzig (W. Grafton and Lillian B. Wilkins Professor of Mechanical Engineering)

  2. Metallurgy Division, USA

    W. J. Boettinger (NIST Fellow)

  3. Thermodynamics and Kinetics Group, Metallurgy Division, USA

    J. A. Warren (Leader)

  4. Mathematical and Computation Sciences Division, Information Technology Laboratory, USA

    G. B. McFadden

  5. the National Institute of Standards and Technology, 20899, Gaithersburg, MD, USA

    S. R. Coriell (Guest Scientist)

  6. Carnegie Mellon University, 15213, Pittsburgh, PA, USA

    R. F. Sekerka (University Professor of Physics, Mathematics and Materials Science)

Authors
  1. J. A. Dantzig
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  2. W. J. Boettinger
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  3. J. A. Warren
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  4. G. B. McFadden
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  5. S. R. Coriell
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  6. R. F. Sekerka
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Dantzig, J.A., Boettinger, W.J., Warren, J.A. et al. Numerical modeling of diffusion-induced deformation. Metall Mater Trans A 37, 2701–2714 (2006). https://doi.org/10.1007/BF02586104

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  • DOI: https://doi.org/10.1007/BF02586104

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